Am using my previous camera Sony AX2000 to shoot and edit in final cut but there is something disturb my mind and i don't know exactly where to fix it. My output video have flickering/shaking like resoulution, see image below

If you look closely to the right hand of this snapshot there is a guy on his back head you see as there is a shake of image. what should i do to overcome this problem regarding camera setting(resolution) and editing setting in a sequence and export setting using .mov or .mp4.

The shaking you describe in your frame grab is actually an interlacing artifact that happens when there is movement. I suspect that the earlier Sony AX2000 is prone to this more so than with newer cameras. The PMW 200 will be much better at interlaced recording and motion artifacts should be reduced to a minimum.

There are various factors that affect how much interlaced 'tearing' is will be visible in your picture:

Generally the faster the shutter speed and the higher the F stop number the less chance of seeing interlacing motion artifacts. If you want to eliminate the artifacts completely then shoot progressive with the PMW 200. With progressive you get one complete picture per frame of video instead of 2 interlacing odd/even fields per frame. With progressive you will get a certain amount of motion blur depending on your shutter speed but this is sometimes desirable depending on what your subject matter is and what 'look' you're trying to achieve. If your final product is to be played on computers or flat screen televisions then shooting progressive is recommended.

In Final Cut Pro if you're shooting interlaced with the PMW 200 then choose an interlaced timeline for your editing with the field order in timeline settings set to upper field first for HD. If you're shooting progressive then obviously choose a progressive timeline.